Final answer:
The correct equation for Jane to determine the fencing distance from her house is (x + x + 40 = 150), which represents the two equal lengths of the fence sides (as 'x') along with the 40-foot house side that are to make up the total of 150 feet of fencing.
Step-by-step explanation:
Jane is going to fence in her back yard with 150 feet of fencing, and she needs to determine how far back from the house she can fence in. The correct equation to represent this situation is option c) (x + x + 40 = 150). We label the unknown sides of the fenced area as 'x'. Since one side of the fencing will be along the back of her house, which is 40 feet, we have two sides remaining to fence with the given 150 feet. If we assume the backyard will have a rectangular shape, we will use two equal lengths of 'x' for the other two sides, plus the 40-foot house side. Therefore, the equation is 2x + 40 = 150 feet, where 2x represents the two sides of fencing equal in length. After solving for 'x', we will get the length of each of the remaining two sides of the fence. To solve for 'x', subtract 40 from both sides of the equation and then divide the result by 2.